The lowest-paid workers would have to get pay rises of at least 25% to compensate for a £5bn cut to tax credits, Labour’s acting leader, Harriet Harman, has said.

Harman pressed the prime minister in the Commons about whether he would cut tax credits by this amount, after he gave a speech on Monday saying he wanted to end the “merry-go-round of welfare” where the state tops up low earnings.

Labour has previously suggested companies could be given tax breaks as an incentive to get them to pay the living wage, which would reduce the tax credit bill.

But Harman criticised Cameron for planning cuts in tax credits without any proposals about how to get companies to raise wages or any apparent thought as to how it would affect children.

“You said in your speech on Monday there is nothing progressive about robbing from our children – but isn’t it inevitable that cuts in tax credit for working families, unless employers raise their wages immediately, mean children will be worse off?” she said. “I’m asking about robbing from children who are in families who are facing tax credit cuts.

“The Institute for Fiscal Studies has said cutting £5bn from tax credits would mean working families losing on average £1,400 a year. I know you don’t have to budget but many families do.”

She said that to compensate for a loss of £1,400 a year, the minimum wage would have to go up overnight by 25%.

Cameron said he wanted to get the unemployed back to work, reduce taxes, encourage higher pay and cut welfare bills as a result.

But Harman hit back: “You don’t get higher pay by cutting tax credits. You seem to be saying low-income families won’t lose out because somehow on the day he cuts tax credits every employer in the country will rush to immediately put up pay.

“To compensate for the loss of tax credits, that would mean employers putting up pay overnight by twice what the OBR has said they are going to do over a full year. That’s not going to happen, is it?”

Without denying repeated suggestions that he wants to cut tax credits, Cameron replied that rates of pay were already going up.

“What you don’t seem to understand is if you don’t get people back to work and reduce welfare you are going to have to make deep cuts in the NHS, which we don’t want to see, or you are going to have to put up taxes, which we don’t want to see,” he said.

“If the Labour party wants to spend this five years arguing against any change in the welfare system, I say let them – you’ll end up with the same result.”

In her final question of the heated exchange, Harman argued that families with children would be worse off. “You say you are tackling low pay: you’re not. You’re attacking the low-paid. So much for the party of working people,” she said.

Cameron replied that the party of working people was “the party that’s got two million more people into work”.